A constant potential difference is applied across a resistance. Consider variation of resistance with temperature. Which graph represents best the variation of power produced in resistance versus resistance?

Options

A.
B.
C.
D.

Explanation

To solve the problem, we need to analyze the relationship between power (P) and resistance (R) when a constant potential difference (V) is applied across the resistance.

### Step-by-Step Solution:

1. **Understand the Power Formula**:
The power (P) dissipated in a resistor when a constant voltage (V) is applied can be expressed using the formula:
\[ P = \frac{V^2}{R} \]
Here, V is constant.

2. **Identify the Relationship**:
From the formula, we can see that power (P) is inversely proportional to resistance (R). This means:
\[ P \propto \frac{1}{R} \]
As resistance increases, power decreases, and as resistance decreases, power increases.

3. **Graphical Representation**:
The relationship \( P \propto \frac{1}{R} \) indicates that if we were to plot power (P) on the y-axis and resistance (R) on the x-axis, the graph would be a hyperbola. This is because an inverse relationship typically results in a hyperbolic curve.

4. **Analyze the Graphs**:
We need to look at the options provided for the graph of power versus resistance. The correct graph should show that as resistance increases, power decreases, which is characteristic of a hyperbolic graph.

5. **Select the Correct Option**:
Upon examining the options, we find that option B displays a hyperbolic curve, where:
- When resistance (R) is low, power (P) is high.
- When resistance (R) is high, power (P) is low.
This matches our derived relationship.

### Conclusion:
The graph that best represents the variation of power produced in resistance versus resistance is option B, which shows a hyperbolic relationship.